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| − | == Problem ==
| + | #REDIRECT [[2006 AIME I Problems/Problem 12]] |
| − | [[Equilateral triangle | Equilateral]] <math> \triangle ABC </math> is inscribed in a [[circle]] of [[radius]] 2. Extend <math> \overline{AB} </math> through <math> B </math> to point <math> D </math> so that <math> AD=13, </math> and extend <math> \overline{AC} </math> through <math> C </math> to point <math> E </math> so that <math> AE = 11. </math> Through <math> D, </math> draw a line <math> l_1 </math> [[parallel]] to <math> \overline{AE}, </math> and through <math> E, </math> draw a line <math> l_2 </math> parallel to <math> \overline{AD}. </math> Let <math> F </math> be the [[intersection]] of <math> l_1 </math> and <math> l_2. </math> Let <math> G </math> be the point on the circle that is [[collinear]] with <math> A </math> and <math> F </math> and distinct from <math> A. </math> Given that the [[area]] of <math> \triangle CBG </math> can be expressed in the form <math> \frac{p\sqrt{q}}{r}, </math> where <math> p, q, </math> and <math> r </math> are [[positive integer]]s, <math> p </math> and <math> r</math> are [[relatively prime]], and <math> q </math> is not [[divisibility | divisible]] by the [[perfect square | square]] of any [[prime]], find <math> p+q+r. </math>
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| − | == Solution ==
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| − | {{solution}}
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| − | == See also ==
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| − | *[[2006 AIME II Problems/Problem 11 | Previous problem]]
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| − | *[[2006 AIME II Problems/Problem 13 | Next problem]]
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| − | *[[2006 AIME II Problems]]
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| − | [[Category:Intermediate Geometry Problems]]
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